A local gift shop sold bags of candy and cookies for Halloween. Bags of candy cost $$5.00$, and bags of cookies cost $$4.50$, and sales equaled $$60.50$ in total. There were $5$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the gift shop.
Solution: Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${5x+4.5y = 60.5}$ ${y = x+5}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+5}$ for $y$ in the first equation. ${5x + 4.5}{(x+5)}{= 60.5}$ Simplify and solve for $x$ $ 5x+4.5x + 22.5 = 60.5 $ $ 9.5x+22.5 = 60.5 $ $ 9.5x = 38 $ $ x = \dfrac{38}{9.5} $ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $ {y = x+5}$ to find $y$ ${y = }{(4)}{ + 5}$ ${y = 9}$ You can also plug ${x = 4}$ into $ {5x+4.5y = 60.5}$ and get the same answer for $y$ ${5}{(4)}{ + 4.5y = 60.5}$ ${y = 9}$ $4$ bags of candy and $9$ bags of cookies were sold.